Re: sorting a nested list of 4-tuples

*To*: mathgroup at smc.vnet.net*Subject*: [mg120399] Re: sorting a nested list of 4-tuples*From*: Ray Koopman <koopman at sfu.ca>*Date*: Thu, 21 Jul 2011 05:48:16 -0400 (EDT)*References*: <j03o4c$a64$1@smc.vnet.net>

On Jul 19, 4:00 am, Luis Valero <luis.val... at mac.com> wrote: > Dear Sirs, > > I want to sort a list of 4-tuples of real numbers, so that, the second 4-tuple has minimum distance to the first, the third, selected from the rest, ha minimum distance to the second, and so on. > > The distance is the euclidean distance, calculated with the first two elements of each 4-tuple. > > I have defined a function that work: > > orderedList[list_] := Module[{nearest}, > Flatten[ Nest[{ > Append[ #[[1]] , nearest = Flatten @@ Nearest[ Map[ Rule[ #[[{1, 2}]], #] &, #[[2]] ], Last[ #[[1]] ] [[{1, 2}]], 1] ], > Delete[ #[[2]], Position[ #[[2]], nearest ] ] } &, { {list[[1]] }, Delete[ list, 1 ] }, Length[ list ] - 2], 1] ]; > > but I need to improve the temporal efficiency > > Thank you This does the job nicely without Nearest. For your real data, change DistanceMatrix@xy to DistanceMatrix[list[[All,{1,2}]]]. n = 10 xy = Table[Random[Real],{n},{2}] ddx = 2 Max[dd = DistanceMatrix@xy]; Do[dd[[i,i]] = ddx,{i,n}]; ddx = Table[ddx,{n}]; NestList[(dd[[#]] = ddx; Ordering[dd[[All,#]],1][[1]])&, 1, n-1] 10 {{0.923827,0.822223}, {0.369167,0.352365}, {0.309981,0.792447}, {0.375829,0.953723}, {0.680294,0.594137}, {0.411011,0.098692}, {0.295584,0.0860474},{0.749339,0.927127}, {0.263566,0.0431098},{0.0684959,0.230974}} {1,8,5,2,6,7,9,10,3,4}